WGCNA Exploratory Analysis

library(tidyverse) ; library(reshape2) ; library(glue) ; library(plotly) ; library(dendextend)
library(RColorBrewer) ; library(viridis) ; require(gridExtra) ; library(GGally) ; library(ggpubr) ; library(ggExtra)
library(WGCNA)
library(expss)
library(polycor)
library(biomaRt)
library(clusterProfiler) # ORA
library(foreach) ; library(doParallel)

SFARI_colour_hue = function(r) {
  pal = c('#FF7631','#FFB100','#E8E328','#8CC83F','#62CCA6','#59B9C9','#b3b3b3','#808080','gray','#d9d9d9')[r]
}

Load preprocessed dataset (preprocessing code in01_data_preprocessing.Rmd) and clustering (pipeline in 05_WGCNA.Rmd)

# Gandal dataset
load('./../Data/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
rownames(datExpr) = datGenes$ensembl_gene_id
datMeta = datMeta %>% mutate(ID = paste0('X',description))


# GO Neuronal annotations: regex 'neuron' in GO functional annotations and label the genes that make a match as neuronal
GO_annotations = read.csv('./../Data/genes_GO_annotations.csv')
GO_neuronal = GO_annotations %>% filter(grepl('neuron', go_term)) %>% 
              mutate('ID'=as.character(ensembl_gene_id)) %>% 
              dplyr::select(-ensembl_gene_id) %>% distinct(ID) %>%
              mutate('Neuronal'=1)


# SFARI Genes
SFARI_genes = read_csv('./../../../SFARI/Data/SFARI_genes_01-03-2020_w_ensembl_IDs.csv')
SFARI_genes = SFARI_genes[!duplicated(SFARI_genes$ID) & !is.na(SFARI_genes$ID),]


# Clusterings
clusterings = read_csv('./../Data/clusters.csv')


# Update DE_info with SFARI and Neuronal information
genes_info = DE_info %>% mutate(ID = datGenes$ensembl_gene_id) %>% 
             dplyr::rename('padj' = adj.P.Val, 'log2FoldChange' = logFC) %>%
             left_join(SFARI_genes, by='ID') %>% 
             mutate(`gene-score`=ifelse(is.na(`gene-score`), 'Others', `gene-score`)) %>%
             distinct(ID, .keep_all = TRUE) %>% left_join(GO_neuronal, by='ID') %>%
             mutate(Neuronal=ifelse(is.na(Neuronal), 0, Neuronal)) %>%
             mutate(gene.score=ifelse(`gene-score`=='Others' & Neuronal==1, 'Neuronal', `gene-score`), 
                    significant=padj<0.05 & !is.na(padj)) %>%
             mutate(Group = factor(ifelse(gene.score %in% c('Neuronal','Others'), gene.score, 'SFARI'), 
                    levels = c('SFARI', 'Neuronal', 'Others'))) %>% left_join(clusterings, by='ID')


rm(DE_info, GO_annotations, clusterings, efit)

---

Dynamic Tree vs Dyamic Hybrid

Comparing module sizes

Dynamic Tree creates less and more balanced modules (opposite to Gandal’s modules)

plot_data = table(genes_info$DynamicTree) %>% data.frame %>% arrange(desc(Freq)) %>% filter(Var1 != 'gray')

p1 = plot_data %>% ggplot(aes(x=reorder(Var1, -Freq), y=Freq)) + 
     geom_bar(stat='identity', fill=plot_data$Var1) + 
     geom_hline(yintercept = mean(plot_data$Freq), color = 'gray',linetype = 'dashed') +
     ggtitle('Modules using Dynamic Tree') + ylab('Number of genes') + xlab('Module') + 
     theme_minimal() + theme(axis.text.x = element_blank())

plot_data = table(genes_info$DynamicHybrid) %>% data.frame %>% arrange(desc(Freq)) %>% filter(Var1 != 'gray')

p2 = plot_data %>% ggplot(aes(x=reorder(Var1, -Freq), y=Freq)) + 
     geom_bar(stat='identity', fill=plot_data$Var1) + 
     geom_hline(yintercept = mean(plot_data$Freq), color = 'gray',linetype = 'dashed') +
     ggtitle('Modules using Dynamic Hybrid') + ylab('Number of genes') + xlab('Module') + 
     theme_minimal() + theme(axis.text.x = element_blank())

grid.arrange(p1,p2, nrow=2, top = 'Comparison of Module sizes')

rm(p1, p2, plot_data)

Comparing genes left without a module

Dynamic Tree leaves 7145 genes without cluster (46%) Dynamic Hybrid leaves 1830 genes without cluster (12%)

Dynamic Tree leaves many more genes without a cluster (too many). As we saw in the dendrograms in 05_WGCNA.html, the genes usually left without a cluster are the ones closest to the root of the dendrogram, now we want to see if they share some characteristic in common: we suspect it may be a weak relation to ASD

• There seems to be a relation between DE and module membership, being DE a more restrictive condition than being assigned to a cluster, but the relation is not as strong as the one found in Gandal

• Genes assigned to a cluster also seem to have a higher level of expression than the genes left unassigned (because they have higher PC1 values)

pca = datExpr %>% prcomp

plot_data = data.frame('ID'=rownames(datExpr), 'PC1' = pca$x[,1], 'PC2' = pca$x[,2]) %>%
            left_join(genes_info, by='ID') %>% mutate('hasCluster' = DynamicTree!='gray', 
                                                      'hasSFARIScore' = `gene-score`!='Others') %>%
            apply_labels(`gene-score` = 'SFARI Gene score', DynamicTree = 'Dynamic Tree Algorithm', 
                         significant = 'Differentially Expressed', hasCluster = 'Belongs to a Module',
                         hasSFARIScore = 'Has a SFARI Score', syndromic = 'Has syndromic tag') %>%
            mutate(alpha_cluster = ifelse(hasCluster==TRUE, 0.8, 0.1),
                   alpha_signif = ifelse(significant==TRUE, 0.8, 0.1))

p1 = plot_data %>% ggplot(aes(PC1, PC2, color=hasCluster)) + geom_point(alpha = plot_data$alpha_cluster) + 
     theme_minimal() + ggtitle('Genes are assigned to a cluster') + theme(legend.position='bottom')

p2 = plot_data %>% ggplot(aes(PC1, PC2, color=significant)) + geom_point(alpha = plot_data$alpha_signif) + 
     theme_minimal() + ggtitle('Genes found to be DE') + theme(legend.position='bottom')

grid.arrange(p1, p2, nrow=1, top = 'Exploring unassigned genes using the Dynamic Tree algorithm')

rm(pca, p1, p2)

Most of the genes that don’t have a cluster are not differentially expressed:

99% of the genes that don’t have a cluster are not differentially expressed

cro(plot_data$significant, list(plot_data$hasCluster, total()))

	Belongs to a Module			#Total
	FALSE	TRUE
Differentially Expressed
FALSE	7097	7716		14813
TRUE	48	597		645
#Total cases	7145	8313		15458

Most of the genes with a SFARI score are not assigned to a cluster:

313 of the SFARI genes (~42%) are not assigned to any cluster

cro(plot_data$hasSFARIScore, list(plot_data$hasCluster, total()))

	Belongs to a Module			#Total
	FALSE	TRUE
Has a SFARI Score
FALSE	6832	7873		14705
TRUE	313	440		753
#Total cases	7145	8313		15458

Conclusion:

The main difference between algorithms is that Dynamic Hybrid clusters outlier genes and Dynamic Tree leaves them out, so Dynamic Tree would give me a ‘cleaner’ group of genes to work with, without losing many SFARI genes, but Dynamic Hybrid has less and more balanced clusters

I think in this case, using the Dynamic Tree modules wouldn’t be feasible given the huge ammount of unassigned genes, so I’m going to use the Dynamic Hybrid algorithm to keep more genes

clustering_selected = 'DynamicHybrid'
genes_info$Module = genes_info[,clustering_selected]

Dynamic Hybrid Modules

*The colour of the modules is the arbitrary one assigned during the WGCNA algorithm, where the gray cluster actually represents all the genes that were left without a cluster (so it’s not actually a cluster).

The Dynamic Hybrid algorithm created 95 modules and leaves 1830 genes without a module (this is still quite large)

table(genes_info$Module)

## 
## #00A4FF #00A7FF #00AAFD #00ADFA #00B0F6 #00B2F2 #00B5EE #00B7E9 #00B813 #00B8E4 
##     100     101     155      42      51     383      35      55     708      31 
## #00B92D #00BA3D #00BADF #00BB4B #00BC56 #00BCDA #00BD61 #00BDD4 #00BE6B #00BECE 
##     184     108     147     124      18      23     211     534      22     452 
## #00BF74 #00BF7D #00BFC1 #00BFC8 #00C086 #00C08E #00C096 #00C0B4 #00C0BA #00C19E 
##     130      51      30      17      65     169     455      33      38     429 
## #00C1A5 #00C1AD #2CB600 #3EA1FF #44B500 #55B300 #5A9DFF #63B200 #6E99FF #6FB000 
##      36      58      70      44     123      21     102     156      28     295 
## #79AF00 #7F96FF #83AD00 #8CAB00 #8E92FF #94A900 #9B8EFF #9CA700 #A3A500 #A789FF 
##     399      31      33     159     490      66      57      95      44     395 
## #AAA300 #B0A100 #B285FF #B69F00 #BC81FF #BC9D00 #C29B00 #C57DFF #C79800 #CC9600 
##      48     112      41      57      78      75     193     370     493     113 
## #CD79FF #D19300 #D575FE #D69100 #DA8E00 #DB72FB #DE8C00 #E26EF7 #E28900 #E68710 
##     139     113     134      24      28      81     382      32     117     234 
## #E76BF3 #E9842C #EC69EE #ED813E #F066EA #F07E4B #F37C58 #F464E4 #F57963 #F863DF 
##      31      69     176     123     575      56      41     182      22      75 
## #F8766D #FA62D9 #FA7477 #FC7180 #FD61D3 #FE61CD #FE6E89 #FF61C6 #FF62BF #FF63B8 
##      17      19      75      29     230      67      45     134     126      42 
## #FF64B1 #FF66A9 #FF68A2 #FF6A9A #FF6C91    gray 
##     195      50     233     139     410    1830

plot_data = table(genes_info$Module) %>% data.frame %>% arrange(desc(Freq))

ggplotly(plot_data %>% ggplot(aes(x=reorder(Var1, -Freq), y=Freq)) + geom_bar(stat='identity', fill=plot_data$Var1) + 
         ggtitle('Module size') + ylab('Number of genes') + xlab('Module') + theme_minimal() + 
         theme(axis.text.x = element_text(angle = 90)))

Relation to external clinical traits

Quantifying module-trait associations

In the WGCNA documentation they use Pearson correlation to calculate correlations, I think all of their variables were continuous. Since I have categorical variables I’m going to use the hetcor function, that calculates Pearson, polyserial or polychoric correlations depending on the type of variables involved.

• I’m not sure how the corPvalueStudent function calculates the p-values and I cannot find any documentation…

• Compared correlations using Pearson correlation and with hetcor and they are very similar, but a bit more extreme with hetcor. The same thing happens with the p-values.

datTraits = datMeta %>% dplyr::select(Diagnosis, Brain_lobe) %>%
            dplyr::rename('Brain Lobe' = Brain_lobe)

# Recalculate MEs with color labels
ME_object = datExpr %>% t %>% moduleEigengenes(colors = genes_info$Module)
MEs = orderMEs(ME_object$eigengenes)

# Calculate correlation between eigengenes and the traits and their p-values
moduleTraitCor = MEs %>% apply(2, function(x) hetcor(x, datTraits)$correlations[1,-1]) %>% t
rownames(moduleTraitCor) = colnames(MEs)
colnames(moduleTraitCor) = colnames(datTraits)
moduleTraitPvalue = corPvalueStudent(moduleTraitCor, nrow(datExpr))

# Create text matrix for the Heatmap
textMatrix = paste0(signif(moduleTraitCor, 2), ' (', signif(moduleTraitPvalue, 1), ')')
dim(textMatrix) = dim(moduleTraitCor)

# In case there are any NAs
if(sum(!complete.cases(moduleTraitCor))>0){
  print(paste0(sum(is.na(moduleTraitCor)),' correlation(s) could not be calculated')) 
}


rm(ME_object)

• In general, modules have strong correlations with Diagnosis with really small p-values and not much relation with brain regions

# Sort moduleTraitCor by Diagnosis
moduleTraitCor = moduleTraitCor[order(moduleTraitCor[,1], decreasing=TRUE),]
moduleTraitPvalue = moduleTraitPvalue[order(moduleTraitCor[,1], decreasing=TRUE),]

# Create text matrix for the Heatmap
textMatrix = paste0(signif(moduleTraitCor, 2), ' (', signif(moduleTraitPvalue, 1), ')')
dim(textMatrix) = dim(moduleTraitCor)


labeledHeatmap(Matrix = moduleTraitCor, xLabels = names(datTraits), yLabels =  gsub('ME','',rownames(moduleTraitCor)), 
               yColorWidth=0, colors = brewer.pal(11,'PiYG'), bg.lab.y = gsub('ME','',rownames(moduleTraitCor)),
               textMatrix = textMatrix, setStdMargins = FALSE, cex.text = 0.8, cex.lab.y = 0.75, zlim = c(-1,1),
               main = paste('Module-Trait relationships'))

diagnosis_cor = data.frame('Module' = gsub('ME','',rownames(moduleTraitCor)),
                           'MTcor' = moduleTraitCor[,'Diagnosis'],
                           'MTpval' = moduleTraitPvalue[,'Diagnosis'])

genes_info = genes_info %>% left_join(diagnosis_cor, by='Module')

rm(moduleTraitCor, moduleTraitPvalue, textMatrix, diagnosis_cor)

Modules with a high Module-Diagnosis (absolute) correlation should have a high content of differentially expressed genes:

This seems to be the case

plot_data = genes_info %>% group_by(Module, MTcor) %>% summarise(p = 100*mean(significant))

plot_data %>% ggplot(aes(MTcor, p)) + geom_hline(yintercept=mean(plot_data$p),color='gray',linetype='dotted') +
              geom_point(color=plot_data$Module, alpha = 0.8, aes(id=Module)) + 
              geom_smooth(color='gray', se=FALSE) + theme_minimal() + 
              xlab('Module-Diagnosis correlation') + ylab('% of DE genes in Module')

Gene Significance and Module Membership

Gene significance: is the value between the correlation between the gene and the trait we are interested in. A positive gene significance means the gene is overexpressed and a negative value means its underexpressed. (The term ‘significance’ is not very acurate because it’s not actually measuring statistical significance, it’s just a correlation, but that’s how they call it in WGCNA…)

Module Membership is the correlation of the module’s eigengene and the expression profile of a gene. The higher the Module Membership, the more similar the gene is to the genes that constitute the module. (I won’t use this measure yet)

Note: Some correlations weren’t able to be calculated with the original function (weirdly because the correlation was too strong), so they are calculated again in the end using the polyserial function instead of hetcor, which is robust enough to calculate them

# It's more efficient to iterate the correlations one by one, otherwise it calculates correlations between the eigengenes and also between the genes, which we don't need

# Check if MM information already exists and if not, calculate it
if(file.exists(paste0('./../Data/dataset_', clustering_selected, '.csv'))){
  
  dataset = read.csv(paste0('./../Data/dataset_', clustering_selected, '.csv'))
  dataset$Module = dataset[,clustering_selected]
  
} else {
  
  ############# 1. Calculate Gene Significance
  GS_info = data.frame('ID'=rownames(datExpr),
                       'GS'=datExpr %>% apply(1, function(x) hetcor(x,datMeta$Diagnosis)$correlations[1,2])) %>%
            mutate('GSpval'=corPvalueStudent(GS, ncol(datExpr)))
  
  #############  2. Calculate Module Membership
  
  #setup parallel backend to use many processors
  cores = detectCores()
  cl = makeCluster(cores-1)
  registerDoParallel(cl)
  
  # Create matrix with MM by gene
  MM = foreach(i=1:nrow(datExpr), .combine=rbind) %dopar% {
    library(polycor)
    tempMatrix = apply(MEs, 2, function(x) hetcor(as.numeric(datExpr[i,]), x)$correlations[1,2])
    tempMatrix
  }
  
  # Stop clusters
  stopCluster(cl)
  
  rownames(MM) = rownames(datExpr)
  colnames(MM) = paste0('MM',gsub('ME','',colnames(MEs)))
  
  # Calculate p-values
  MMpval = MM %>% corPvalueStudent(ncol(datExpr)) %>% as.data.frame
  colnames(MMpval) = paste0('MMpval', gsub('ME','',colnames(MEs)))
  
  MM = MM %>% as.data.frame %>% mutate(ID = rownames(.))
  MMpval = MMpval %>% as.data.frame %>% mutate(ID = rownames(.))
  
  # Join and save results
  dataset = genes_info %>% dplyr::select(ID, `gene-score`, clustering_selected, MTcor, MTpval) %>%
            left_join(GS_info, by='ID') %>%
            left_join(MM, by='ID') %>%
            left_join(MMpval, by='ID')
  
  write.csv(dataset, file = paste0('./../Data/dataset_', clustering_selected, '.csv'), row.names = FALSE)
  
  rm(cores, cl) 
  
}

GS_missing = dataset$ID[is.na(dataset$GS)] %>% as.character

if(length(GS_missing)>0){
  
  cat(paste0(length(GS_missing),' correlations between genes and Diagnosis could not be calculated, ',
             'calculating them with the polyserial function'))
  
  for(g in GS_missing){
    dataset$GS[dataset$ID == g] = polyserial(as.numeric(datExpr[g,]), datMeta$Diagnosis)
  }
  
}

rm(GS_missing)

Analysing concordance between these metrics in the genes

1. Gene Significance vs Log Fold Change

Gene significance and Log Fold Chance are two different ways to measure the same thing, so there should be a concordance between them

Both variables agree with each other relatively well

plot_data = dataset %>% dplyr::select(ID, MTcor, GS) %>% 
            left_join(genes_info %>% dplyr::select(ID, gene.score), by='ID') %>%
            left_join(genes_info %>% dplyr::select(ID,AveExpr,log2FoldChange,significant,Module), by='ID') %>%
            left_join(data.frame(MTcor=unique(dataset$MTcor)) %>% arrange(by=MTcor) %>% 
                                 mutate(order=1:length(unique(dataset$MTcor))), by='MTcor')

ggplotly(plot_data %>% ggplot(aes(GS, log2FoldChange)) +
         geom_point(color=plot_data$Module, alpha=0.5, aes(ID=Module)) + 
         geom_smooth(color='gray', se=FALSE) + theme_minimal() + xlab('Gene Significance') + 
         ggtitle(paste0('R^2 = ', round(cor(plot_data$log2FoldChange, plot_data$GS)[1]**2, 2))))

2. Module-Diagnosis correlation vs Gene Significance

In general, modules with the highest Module-Diagnosis correlation should have genes with high Gene Significance

Note: For the Module-Diagnosis plots, if you do boxplots, you lose the exact module-diagnosis correlation and you only keep the order, so I decided to compensate this downside with a second plot, where each point is plotted individually using their module’s Module-Diagnosis correlation as the x axis. I think the boxplot plot is easier to understand but the second plot contains more information, so I don’t know which one is better.

plot_data = plot_data %>% arrange(order)

ggplotly(plot_data %>% ggplot(aes(order, GS, group=order)) + 
         geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + theme_minimal() + 
         xlab('Modules ordered by Module-Diagnosis correlation') + ylab('Gene Significance'))

## Warning: `group_by_()` is deprecated as of dplyr 0.7.0.
## Please use `group_by()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

plot_data %>% ggplot(aes(MTcor, GS)) + geom_hline(yintercept=0, color='gray', linetype='dotted') + 
         geom_point(color=plot_data$Module, alpha=0.1, aes(id=ID)) + geom_smooth(color='gray', se=FALSE) + 
         theme_minimal() + xlab('Module-Diagnosis correlation') + ylab('Gene Significance') + 
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, plot_data$GS)^2,2)))

3. Module-Diagnosis correlation vs Log Fold Change

The same happens with the Log Fold Change

ggplotly(plot_data %>% ggplot(aes(order, log2FoldChange, group=order)) + 
         geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + 
         theme_minimal() + xlab('Modules ordered by Module-Diagnosis correlation') + ylab('log2FoldChange'))

ggplotly(plot_data %>% ggplot(aes(MTcor, log2FoldChange)) + 
         geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_point(color=plot_data$Module, alpha=0.1, aes(id=ID)) + geom_smooth(color='gray', se=FALSE) + 
         theme_minimal() + xlab('Module-Diagnosis correlation') + ylab('log2FoldChange') + 
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, plot_data$log2FoldChange)^2,2))))

4. Module-Diagnosis vs Mean Expression

ggplotly(plot_data %>% ggplot(aes(order, log2(AveExpr+1), group=order)) + 
         geom_hline(yintercept=mean(log2(plot_data$AveExpr+1)), color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + theme_minimal() + 
         xlab('Modules ordered by Module-Diagnosis correlation') + ylab('log2(Mean Expression)'))

plot_data %>% ggplot(aes(MTcor, log2(AveExpr+1))) + geom_point(alpha=.2, color=plot_data$Module, aes(id=ID)) + 
         geom_hline(yintercept=mean(log2(plot_data$AveExpr+1)), color='gray', linetype='dotted') + 
         geom_smooth(color='gray', alpha=0.3) + theme_minimal() + 
         xlab('Module-Diagnosis correlation') + ylab('log2(Mean Expression)') +
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, log2(plot_data$AveExpr+1))^2,2)))

Conclusion:

All of the variables seem to agree with each other, Modules with a high correlation with Diagnosis tend to have genes with high values of Log Fold Change as well as high values of Gene Significance, and the gray module, which groups all the genes that weren’t assigned to any cluster tends to have a very poor performance in all of the metrics.

---

SFARI Scores

Since SFARI scores genes depending on the strength of the evidence linking it to the development of autism, in theory, there should be some concordance between the metrics we have been studying above and these scores…

SFARI Scores vs Gene Significance

comparisons = list(c('1','2'), c('2','3'), c('3','Neuronal'), c('Neuronal','Others'),
                   c('1','3'), c('3','Others'), c('2','Neuronal'),
                   c('1','Neuronal'), c('2','Others'), c('1','Others'))
increase = 0.04
base = 0.66
pos_y_comparisons = c(rep(base, 4), rep(base + increase, 2), base + 2:5*increase)

plot_data %>% ggplot(aes(gene.score, abs(GS), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .01) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:3,8,7))) + theme_minimal() + 
              ylab('Gene Significance Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Scores vs Module-Diagnosis correlation

Note: Filtering out gray module because otherwise too many genes share the same Module-Diagnosis correlation

increase = 0.05
base = 0.97
pos_y_comparisons = c(rep(base, 4), rep(base + increase, 2), base + 2:5*increase)

plot_data %>% filter(Module != 'gray') %>% ggplot(aes(gene.score, abs(MTcor), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .01) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:3,8,7))) + theme_minimal() + 
              ylab('Module-Diagnosis Correlation Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Enrichment vs Module-Diagnosis correlation

To study the strength of the relationship between a module and the biological signal found in the data related to ASD we have the Module-Diagnosis metric. We want to do a similar thing to calculate the ‘strength’ of the presence of SFARI Genes in each module to be able to identify the modules ‘enriched’ in SFARI Genes

The easiest metric would be to calculate the percentage of genes in each module that belong to the SFARI Genes, but this metric doesn’t take into account the size of the model and can favour more extreme but less robust results (small modules)

Instead, we are going to use the Over Representation Analysis (ORA) approach, that uses the hypergeometric distribution to calculate the probability of a module of size \(n\) containing at least \(k\) SFARI Genes and we are going to interpret this probability as the ‘enrichment’ of SFARI Genes in each module

Hypergeometric distribution explanation:

If we interpret the number of genes (\(n\)) in a cluster as \(n\) random draws without replacement from a finite population of size \(N\), and the number of SFARI genes in the cluster (\(s\)) as \(s\) successes in those \(n\) draws, where we know that \(N\) contains exactly \(S\) successes, then we can use the hypergeometric distribution to calculate the statistical significance of having drawn \(s\) successes out of \(n\) draws, and use this value to select the clusters with the highest statistical significance

Percentage of SFARI Genes vs ORA by Module

# Calculate % and ORA of SFARI Genes in each module

modules = unique(genes_info$Module[genes_info$Module!='gray']) %>% as.character

# We need the entrez ID of the genes for this
getinfo = c('ensembl_gene_id','entrezgene')
mart = useMart(biomart='ENSEMBL_MART_ENSEMBL', dataset='hsapiens_gene_ensembl', 
               host='feb2014.archive.ensembl.org')
biomart_output = getBM(attributes=getinfo, filters=c('ensembl_gene_id'), 
                       values=genes_info$ID[genes_info$Module!='gray'], mart=mart) %>%
                 left_join(genes_info %>% dplyr::select(ID, Module,`gene-score`), by = c('ensembl_gene_id'='ID'))

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>% mutate(term = ifelse(`gene-score` == 'Others', 'Others', 'SFARI'), 
                                      'gene' = entrezgene) %>%  dplyr::select(term, gene) %>% distinct


enrichment_data = data.frame('Module' = modules, 'size' = 0, 'perc_SFARI' = 0,
                             'pval_ORA' = 0, 'padj_ORA' = 0)

for(i in 1:length(modules)){
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 50000) %>% 
                        data.frame %>% dplyr::select(-geneID,-Description)
  ORA_pval = ifelse('SFARI' %in% ORA_module$ID, ORA_module$pvalue[ORA_module$ID=='SFARI'], 1)
  ORA_padj = ifelse('SFARI' %in% ORA_module$ID, ORA_module$p.adjust[ORA_module$ID=='SFARI'], 1)
  enrichment_data[i,-1] = c(length(genes_in_module), 
                            mean(genes_info$`gene-score`[genes_info$Module==module]!='Others'), 
                            ORA_pval, ORA_padj)
}

enrichment_data = enrichment_data %>% 
                  left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')

rm(i, module, genes_in_module, ORA_module, ORA_pval, ORA_padj, getinfo, mart, term2gene)

Note: in ORA, a lower probability indicates a higher enrichment in SFARI Genes, so I’m using 1-probability to measure the enrichment of each module

The two metrics agree quite well, but if we focus on the modules with the highest ‘enrichment’ with both metrics we can see that the smallest modules are below the trend line while the larger ones are above, which shows the bias towards small modules the percentage of SFARI Genes metric has, making the ORA Enrichment metric more desirable

ggplotly(enrichment_data %>% ggplot(aes(perc_SFARI, 1-pval_ORA, size=size)) + 
         geom_point(color = enrichment_data$Module, alpha = 0.5, aes(id=Module)) + 
         geom_smooth(color='gray', se = FALSE) + 
         xlab('% of SFARI Genes') + ylab('ORA Enrichment') + ggtitle('Modules') + theme_minimal())

SFARI Enrichment vs Module-Diagnosis Correlation

Cor(SFARI Enrichment, Module-Diagnosis) = 0.14

• Correlation for modules with a positive Module-Diagnosis correlation = -0.1

• Correlation for modules with a negative Module-Diagnosis correlation = 0.07

ggplotly(enrichment_data %>% ggplot(aes(MTcor, 1-pval_ORA, size=size)) + 
         geom_point(color=enrichment_data$Module, alpha=0.5, aes(id=Module)) + 
         geom_smooth(color='#cccccc', size = 0.5, alpha=0.1) + xlab('Module-Diagnosis Correlation') + 
         ggtitle('SFARI Enrichment vs Module-Diagnosis Correlation') +
         ylab('Enrichment in SFARI Genes') + theme_minimal() + theme(legend.position = 'none'))

# Save for comparison with old SFARI Genes
enrichment_data_new_SFARI = enrichment_data

Dividing the SFARI Genes by score we get the same pattern, just noisier because the groups are smaller now

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>%
            mutate('term' = ifelse(`gene-score` == 'Others', 'Others', `gene-score`), 
                   'gene' = entrezgene) %>% dplyr::select(term, gene) %>% distinct


enrichment_data_by_score = data.frame('Module' = as.character(), 'size' = as.numeric(), 
                                      'SFARI_score' = as.character(), 'pval_ORA' = as.numeric(), 
                                      'padj_ORA' = as.numeric())

SFARI_scores = SFARI_genes$`gene-score` %>% table %>% names

for(i in 1:length(modules)){
  
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 1e3)
  
  if(length(ORA_module)>0){
    ORA_module = ORA_module %>% data.frame %>% dplyr::select(ID, pvalue, p.adjust) %>%
                 add_column(.before = 'ID', Module = module) %>% 
                 add_column(.before = 'ID', size = length(genes_in_module)) %>%
                 dplyr::rename('SFARI_score' = ID, 'pval_ORA' = pvalue, 'padj_ORA' = p.adjust)
    
    missing_scores = SFARI_scores[!SFARI_scores %in% ORA_module$SFARI_score]
  } else{
    missing_scores = SFARI_scores
  }
  
  if(length(missing_scores)>0){
    for(ms in missing_scores) ORA_module = rbind(ORA_module, c(module, length(genes_in_module), ms, 1, 1))
  }
  
  colnames(ORA_module) = c('Module','size','SFARI_score','pval_ORA','padj_ORA')
  
  enrichment_data_by_score = rbind(enrichment_data_by_score, ORA_module)
}


enrichment_data_by_score = enrichment_data_by_score %>% 
                           left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')


enrichment_data_by_score = enrichment_data_by_score %>% 
                  mutate(color = SFARI_colour_hue(r = 1:3)[SFARI_score %>% as.numeric])

ggplotly(enrichment_data_by_score %>% 
         ggplot(aes(MTcor, 1-as.numeric(pval_ORA), size=size, color = color, fill = color)) + 
         geom_point(alpha=0.5, aes(id=Module)) + geom_smooth(size = 0.5, alpha = 0.1) +
         xlab('Module-Diagnosis Correlation') + ylab('Enrichment') + 
         scale_colour_manual(values = SFARI_colour_hue(r=1:3)) +
         scale_fill_manual(values = SFARI_colour_hue(r=1:3)) + 
         ggtitle('Enrichment by SFARI Gene Score') + 
         theme_minimal() + theme(legend.position = 'none'))

rm(i, module, genes_in_module, ORA_module, term2gene, SFARI_scores, missing_scores, ms, enrichment_data_by_score)

Old SFARI Scores

# SFARI Genes
SFARI_genes = read_csv('./../../../SFARI/Data/SFARI_genes_08-29-2019_w_ensembl_IDs.csv')
SFARI_genes = SFARI_genes[!duplicated(SFARI_genes$ID) & !is.na(SFARI_genes$ID),]

plot_data = plot_data %>% dplyr::select(-gene.score) %>% 
            left_join(SFARI_genes %>% dplyr::select(ID, `gene-score`), by = 'ID') %>%
            mutate(gene.score = ifelse(!is.na(`gene-score`), `gene-score`, 
                                       ifelse(ID %in% GO_neuronal$ID, 'Neuronal', 'Others')))

SFARI Scores vs Gene Significance

• SFARI Score 6 has the highest median of all groups of genes (!)

• Neuronal annotated genes have higher Gene Significance than genes without any neuronal-related annotation (makes sense)

• These differences are generally not statistically significant, but it could be because in part because there are very few genes in each of the SFARI scores

comparisons = list(c('1','2'), c('2','3'), c('3','4'), c('4','5'), c('5','6'), c('6','Neuronal'), c('Neuronal','Others'),
                   c('1','3'), c('3','5'), c('5','Neuronal'), 
                   c('2','4'), c('4','6'), c('6','Others'),
                   c('1','4'), c('4','Neuronal'),
                   c('2','5'), c('5','Others'),
                   c('3','Neuronal'), c('1','5'), c('2','6'), c('3','Neuronal'), c('4','Others'))
increase = 0.04
base = 0.7
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
                      rep(base + 4*increase, 2), base + 5:9*increase)

plot_data %>% ggplot(aes(gene.score, abs(GS), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .01) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() + 
              ylab('Gene Significance Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Scores vs Module-Diagnosis correlation

• SFARI Scores 2 to 5 have similar distributions

• SFARI Score 6 has the highest Module-Diagonsis correlation magnitude distribution. It seems to have a distribution different to the rest of the SFARI genes

• SFARI Score 1 also has a high Module-Diagnosis correlation magnitude distribution

• The group with the highest Module-Diagnosis correlation is SFARI score 6, which is supposed to be the one with the least amount of evidence suggesting a relation to autism (!)

• Most differences are not statistically significant

increase = 0.05
base = .95
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
                      rep(base + 4*increase, 2), base + 5:9*increase)

plot_data %>% filter(Module != 'gray') %>% ggplot(aes(gene.score, abs(MTcor), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .01) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() + 
              ylab('Module-Diagnosis Correlation Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Enrichment vs Module-Diagnosis correlation

Percentage of SFARI Genes vs ORA by Module

# Calculate % and ORA of SFARI Genes in each module

# update biomart_output SFARI labels
biomart_output = biomart_output %>% dplyr::select(-`gene-score`) %>%
                 left_join(plot_data %>% dplyr::select(ID, `gene-score`), by = c('ensembl_gene_id'='ID'))

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>% mutate(term = ifelse(is.na(`gene-score`), 'Others', 'SFARI'), 
                                      'gene' = entrezgene) %>%  dplyr::select(term, gene) %>% distinct


enrichment_data = data.frame('Module' = modules, 'size' = 0, 'perc_SFARI' = 0,
                       'pval_ORA' = 0, 'padj_ORA' = 0)

for(i in 1:length(modules)){
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 50000) %>% 
                        data.frame %>% dplyr::select(-geneID,-Description)
  ORA_pval = ifelse('SFARI' %in% ORA_module$ID, ORA_module$pvalue[ORA_module$ID=='SFARI'], 1)
  ORA_padj = ifelse('SFARI' %in% ORA_module$ID, ORA_module$p.adjust[ORA_module$ID=='SFARI'], 1)
  enrichment_data[i,-1] = c(length(genes_in_module), 
                          mean(!is.na(plot_data$`gene-score`[plot_data$Module==module])), 
                          ORA_pval, ORA_padj)
}

enrichment_data = enrichment_data %>% 
                  left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')

rm(i, module, genes_in_module, ORA_module, ORA_pval, ORA_padj, getinfo, mart, term2gene)

Note: in ORA, a lower probability indicates a higher enrichment in SFARI Genes, so I’m using 1-probability to measure the enrichment of each module

The two metrics agree quite well, but if we focus on the modules with the highest ‘enrichment’ with both metrics we can see that the smallest modules are below the trend line while the larger ones are above, which shows the bias towards small modules the percentage of SFARI Genes metric has, making the ORA Enrichment metric more desirable

ggplotly(enrichment_data %>% ggplot(aes(perc_SFARI, 1-pval_ORA, size=size)) + 
         geom_point(color = enrichment_data$Module, alpha = 0.5, aes(id=Module)) + 
         geom_smooth(color='gray', se = FALSE) + 
         xlab('% of SFARI Genes') + ylab('ORA Enrichment') + ggtitle('Modules') + theme_minimal())

SFARI Enrichment vs Module-Diagnosis Correlation

Cor(SFARI Enrichment, Module-Diagnosis) = 0.14

• Correlation for modules with a positive Module-Diagnosis correlation = 0.01

• Correlation for modules with a negative Module-Diagnosis correlation = 0.15

ggplotly(enrichment_data %>% ggplot(aes(MTcor, 1-pval_ORA, size=size)) + 
         geom_point(color=enrichment_data$Module, alpha=0.5, aes(id=Module)) + 
         geom_smooth(color='#cccccc', size = 0.5, alpha=0.1) + xlab('Module-Diagnosis Correlation') + 
         ggtitle('SFARI Enrichment vs Module-Diagnosis Correlation') +
         ylab('Enrichment in SFARI Genes') + theme_minimal() + theme(legend.position = 'none'))

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>%
            mutate('term' = ifelse(`gene-score` == 'Others', 'Others', `gene-score`), 
                   'gene' = entrezgene) %>% dplyr::select(term, gene) %>% distinct


enrichment_data_by_score = data.frame('Module' = as.character(), 'size' = as.numeric(), 
                                      'SFARI_score' = as.character(), 'pval_ORA' = as.numeric(), 
                                      'padj_ORA' = as.numeric())

SFARI_scores = SFARI_genes$`gene-score` %>% table %>% names

for(i in 1:length(modules)){
  
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 1e3)
  
  if(length(ORA_module)>0){
    ORA_module = ORA_module %>% data.frame %>% dplyr::select(ID, pvalue, p.adjust) %>%
                 add_column(.before = 'ID', Module = module) %>% 
                 add_column(.before = 'ID', size = length(genes_in_module)) %>%
                 dplyr::rename('SFARI_score' = ID, 'pval_ORA' = pvalue, 'padj_ORA' = p.adjust)
    
    missing_scores = SFARI_scores[!SFARI_scores %in% ORA_module$SFARI_score]
  } else{
    missing_scores = SFARI_scores
  }
  
  if(length(missing_scores)>0){
    for(ms in missing_scores) ORA_module = rbind(ORA_module, c(module, length(genes_in_module), ms, 1, 1))
  }
  
  colnames(ORA_module) = c('Module','size','SFARI_score','pval_ORA','padj_ORA')
  
  enrichment_data_by_score = rbind(enrichment_data_by_score, ORA_module)
}


enrichment_data_by_score = enrichment_data_by_score %>% 
                           left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')


enrichment_data_by_score = enrichment_data_by_score %>% 
                  mutate(color = SFARI_colour_hue(r = 1:6)[SFARI_score %>% as.numeric])

ggplotly(enrichment_data_by_score %>% 
         ggplot(aes(MTcor, 1-as.numeric(pval_ORA), size=size, color = color, fill = color)) + 
         geom_point(alpha=0.3, aes(id=Module)) + geom_smooth(size = 0.5, alpha = 0.05) +
         xlab('Module-Diagnosis Correlation') + ylab('Enrichment') + 
         scale_colour_manual(values = SFARI_colour_hue(r=1:6)) +
         scale_fill_manual(values = SFARI_colour_hue(r=1:6)) + 
         ggtitle('Enrichment by SFARI Gene Score') + 
         theme_minimal() + theme(legend.position = 'none'))

rm(i, module, genes_in_module, ORA_module, term2gene, SFARI_scores, missing_scores, ms, enrichment_data_by_score)

Comparison between Old and New SFARI Genes

• With both SFARI Gene lists, there seems to be a correlation between Mdoule-Diagnosis correlation and SFARI Enrichment in modules with negative Module-Diagnosis correlation

• In the histogram on the right we can see that the enrichment for the new SFARI Genes is slightly weaker (with higher density close to zero) than the old SFARI Genes

compare_plot = enrichment_data %>% dplyr::mutate('Old_SFARI' = pval_ORA) %>% 
               dplyr::select(Module, size, MTcor, Old_SFARI) %>%
               left_join(enrichment_data_new_SFARI %>% dplyr::mutate('New_SFARI' = pval_ORA) %>%
                         dplyr::select(Module, New_SFARI), by = 'Module') %>% 
               melt(id.vars = c('Module','size','MTcor')) %>% dplyr::rename('SFARI_version' = variable) %>%
               mutate(size = sqrt(100*as.numeric(size)/max(as.numeric(size))))

p = compare_plot %>% ggplot(aes(MTcor, 1-as.numeric(value), color = SFARI_version, fill = SFARI_version)) +
    geom_point(alpha = 0.5, size=compare_plot$size, aes(id=Module)) + geom_smooth(alpha = 0.1) + 
    xlab('Module-Diagnosis Correlation') + ylab('Enrichment in SFARI Genes') + 
    ggtitle('SFARI Enrichment vs Module-Diagnosis Correlation') +
    theme_minimal() + theme(legend.position = 'bottom')
          
ggExtra::ggMarginal(p, type = 'density', margins = 'y', groupColour = TRUE, groupFill = TRUE, size=10)

rm(p, compare_plot)

Conclusion:

• SFARI genes not consistent with the other measurements, they even sometimes seem to contradict them, although the strength of the relations is usually not strong enough to be statistically significant

• These patterns are visible in both old and new SFARI Scoring systems, but they are perhaps a bit clearer with the old SFARI scoring system

Session info

sessionInfo()

## R version 3.6.3 (2020-02-29)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.4 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
## 
## locale:
##  [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_GB.UTF-8    
##  [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8   
##  [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] parallel  stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] doParallel_1.0.15      iterators_1.0.12       foreach_1.5.0         
##  [4] clusterProfiler_3.12.0 biomaRt_2.40.5         polycor_0.7-10        
##  [7] expss_0.10.2           WGCNA_1.69             fastcluster_1.1.25    
## [10] dynamicTreeCut_1.63-1  ggExtra_0.9            ggpubr_0.2.5          
## [13] magrittr_1.5           GGally_1.5.0           gridExtra_2.3         
## [16] viridis_0.5.1          viridisLite_0.3.0      RColorBrewer_1.1-2    
## [19] dendextend_1.13.4      plotly_4.9.2           glue_1.4.1            
## [22] reshape2_1.4.4         forcats_0.5.0          stringr_1.4.0         
## [25] dplyr_1.0.0            purrr_0.3.4            readr_1.3.1           
## [28] tidyr_1.1.0            tibble_3.0.1           ggplot2_3.3.2         
## [31] tidyverse_1.3.0       
## 
## loaded via a namespace (and not attached):
##   [1] readxl_1.3.1          backports_1.1.8       fastmatch_1.1-0      
##   [4] Hmisc_4.4-0           igraph_1.2.5          plyr_1.8.6           
##   [7] lazyeval_0.2.2        splines_3.6.3         crosstalk_1.1.0.1    
##  [10] BiocParallel_1.18.1   urltools_1.7.3        digest_0.6.25        
##  [13] GOSemSim_2.10.0       htmltools_0.4.0       GO.db_3.8.2          
##  [16] fansi_0.4.1           checkmate_2.0.0       memoise_1.1.0        
##  [19] cluster_2.1.0         graphlayouts_0.7.0    modelr_0.1.6         
##  [22] matrixStats_0.56.0    enrichplot_1.4.0      prettyunits_1.1.1    
##  [25] jpeg_0.1-8.1          colorspace_1.4-1      ggrepel_0.8.2        
##  [28] blob_1.2.1            rvest_0.3.5           haven_2.2.0          
##  [31] xfun_0.12             crayon_1.3.4          RCurl_1.98-1.2       
##  [34] jsonlite_1.7.0        impute_1.58.0         survival_3.1-12      
##  [37] polyclip_1.10-0       gtable_0.3.0          UpSetR_1.4.0         
##  [40] BiocGenerics_0.30.0   scales_1.1.1          DOSE_3.10.2          
##  [43] mvtnorm_1.1-0         DBI_1.1.0             miniUI_0.1.1.1       
##  [46] Rcpp_1.0.4.6          xtable_1.8-4          progress_1.2.2       
##  [49] htmlTable_1.13.3      gridGraphics_0.5-0    europepmc_0.4        
##  [52] foreign_0.8-76        bit_1.1-15.2          preprocessCore_1.46.0
##  [55] Formula_1.2-3         stats4_3.6.3          htmlwidgets_1.5.1    
##  [58] httr_1.4.1            fgsea_1.10.1          acepack_1.4.1        
##  [61] ellipsis_0.3.1        farver_2.0.3          pkgconfig_2.0.3      
##  [64] reshape_0.8.8         XML_3.99-0.3          nnet_7.3-14          
##  [67] dbplyr_1.4.2          labeling_0.3          ggplotify_0.0.5      
##  [70] tidyselect_1.1.0      rlang_0.4.6           later_1.0.0          
##  [73] AnnotationDbi_1.46.1  munsell_0.5.0         cellranger_1.1.0     
##  [76] tools_3.6.3           cli_2.0.2             generics_0.0.2       
##  [79] RSQLite_2.2.0         ggridges_0.5.2        broom_0.5.5          
##  [82] evaluate_0.14         fastmap_1.0.1         yaml_2.2.1           
##  [85] knitr_1.28            bit64_0.9-7           fs_1.4.0             
##  [88] tidygraph_1.2.0       ggraph_2.0.3          nlme_3.1-147         
##  [91] mime_0.9              DO.db_2.9             xml2_1.2.5           
##  [94] compiler_3.6.3        rstudioapi_0.11       curl_4.3             
##  [97] png_0.1-7             ggsignif_0.6.0        reprex_0.3.0         
## [100] tweenr_1.0.1          stringi_1.4.6         lattice_0.20-41      
## [103] Matrix_1.2-18         vctrs_0.3.1           pillar_1.4.4         
## [106] lifecycle_0.2.0       BiocManager_1.30.10   triebeard_0.3.0      
## [109] cowplot_1.0.0         data.table_1.12.8     bitops_1.0-6         
## [112] qvalue_2.16.0         httpuv_1.5.2          R6_2.4.1             
## [115] latticeExtra_0.6-29   promises_1.1.0        IRanges_2.18.3       
## [118] codetools_0.2-16      MASS_7.3-51.6         assertthat_0.2.1     
## [121] withr_2.2.0           S4Vectors_0.22.1      mgcv_1.8-31          
## [124] hms_0.5.3             grid_3.6.3            rpart_4.1-15         
## [127] rvcheck_0.1.8         rmarkdown_2.1         ggforce_0.3.1        
## [130] Biobase_2.44.0        shiny_1.4.0.2         lubridate_1.7.4      
## [133] base64enc_0.1-3